The present disclosure relates to systems and methods for medical image data preparation and/or reconstruction. More particularly, systems and method are provided for processing medical imaging data to promote consistency and reconstruct images with controlled artifacts.
With conventional image reconstruction techniques, such as filtered backprojection for multi-detector CT (MDCT), C-arm cone beam CT (CBCT) imaging, CBCT for radiation therapy guidance, and Fourier-based reconstructions techniques for magnetic resonance imaging (MRI), a single image is reconstructed from a corresponding set of data acquired with the medical imaging system. For example, one image is reconstructed from a single sinogram in x-ray MDCT, CBCT imaging and one image is reconstructed from one k-space data set in MRI. This correspondence between data and the images reconstructed from that data is a function of traditional image reconstruction techniques and the fact that such techniques are based on an assumption that all of the acquired data are consistent with each other. Routinely, however, data acquired with medical imaging systems are not consistent with a single true image of the subject being imaged, or a single state of a true image object that has dynamic characteristics.
These inconsistencies manifest as artifacts in the reconstructed images and can have many different origins. For example, in x-ray MDCT and CBCT imaging, artifacts can result from the use of polychromatic x-ray spectrum in data acquisition, the presence of metal objects in the subject, by acquiring too few projections, from beam-hardening effects, from x-ray scatters, subject motion including cardiac motion, respiratory motion, and inadvertent body motion during data acquisitions, and so on. In MRI, artifacts can result from undersampling k-space, receiver coil sensitivity, magnetic field inhomogeneities, subject motion, and so on. Inconsistencies between the acquired data and the stationary state of a true image of the subject can also have other sources, such as the presence of an exogenous contrast agent that administered to the subject and the dynamic uptakes through the subject's vasculature. The assumption that the reconstructed image should be consistent with the acquired data is embodied in the following imaging model:AI=Y  (1);
which states that image reconstruction techniques should seek to reconstruct an image, I, that when forward projected match with the acquired data, Y. The matrix, A, is referred to as the system matrix, which can be generally regarded as a forward projection operator that relates the reconstructed image, I, to the acquired data samples, Y. Eqn. (1) imposed that the reconstructed image, I, must be consistent with the measured data samples, Y; thus, Eqn. (1) can also be referred to as the “data consistency condition.” In x-ray CT imaging, the system matrix can include a reprojection operation and in MRI the system matrix can include a Fourier transform operation. The consistency condition of Eqn. (1), put in other words, states that when an image is faithfully reconstructed, the forward projection of that image should be substantially similar to, or consistent with, the data actually acquired with the imaging system.
Additionally, to reconstruct an image, I, from the measured data, Y, it is often required that the data satisfy the so-called data sufficiency condition, which is a condition that allows for an inverse reconstruction formula to be used to reconstruct the image from the measured data. In x-ray CT imaging, the data sufficiency condition is the so-called Tuy condition, which requires the data samples to be acquired in an extended angular range around the image object. In MRI, the data sufficiency condition is the complete population of the entire Fourier space.
Even when the data sufficiency condition is satisfied, however, still another condition needs to be met to reconstruct a true image of the image object. The discretely acquired data samples also need to satisfy the associated sampling criterion for a given reconstruction scheme and be sufficiently consistent with itself. Examples of data sampling criteria include the view angle sampling requirement in x-ray CT and the Nyquist sampling criterion in MRI.
When the data sufficiency condition and data sampling criterion are met in x-ray CT, filtered backprojection can be used to reconstruct an image, and when both data sufficiency condition and data sampling criterion are met in MRI, Fourier inversion can be used to reconstruct an image.
When an iterative image reconstruction method is employed, the data sufficiency condition and data sampling criteria can be relaxed to some extent. One example of such a method is compressed sensing based iterative image reconstruction techniques.
In an ideal situation, when the aforementioned data sufficiency condition and data sampling conditions are satisfied, an artifact-free image can be reconstructed. This ideal situation is impractical in the real world, however, due to the non-ideal nature of all the hardware data acquisition systems and complications from the objects being imaged. As a result of these complications, the acquired data may not represent the same physical state of the image object, or may not be acquired under the same physical conditions. Thus, the acquired data are referred to as “inconsistent data.” That is, such inconsistent data lacks consistency within and between the data, beyond any data sufficiency and sampling issues. The physical reasons for these inconsistencies, whether because of a non-ideal acquisition system or because of a change in the physical state of the object during data acquisition, are referred to as the sources of inconsistency.
When the acquired data are no longer consistent due to sources of inconsistency, such as those described above, the consistency condition begins to break down. That is, the acquired data are no longer consistent when physical effects such as subject motion, contrast enhancement, noise, beam hardening in x-ray imaging, and so on are present during the data acquisition process. The inconsistencies in the acquired data manifest as artifacts in the reconstructed images.
Although a qualitative correlation between data inconsistency and the resultant image artifacts is known, there are no widely-accepted, systematic ways to quantify the relationship between artifacts and data inconsistency levels, or to develop image reconstruction algorithms that incorporate data consistency evaluation and classification into reconstruction process to sufficiently mitigate image artifacts caused by the many different types and causes of data inconsistency. At best, in the case of CT imaging, some have provided mathematical data consistency conditions for the entire set of line integrals of attenuation coefficients for parallel-beam line integrals and divergent fan-beam line integrals, and these conditions have been utilized as guiding principle to either complete the missing line integrals or to compensate for object movement during the data acquisition process. These characterizations of data consistency are referred to as global characterizations since they do not tell whether one specific datum is consistent with others, or one view of data is consistent with data acquired at other view angles.
Thus, a need persists to invent new methods that are able to characterize intrinsic data consistency level from one datum to another or from one view of data to another view of data and to incorporate the new data consistency classification method into image reconstruction to produce medical and other images that are free from or otherwise not corrupted by artifacts, despite inconsistent data and/or undersampled data.